Like Charge Attraction through Hydrodynamic Interaction

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Todd M. Squires and Michael P. Brenner Phys. Rev. Lett. 85, 4976-4979 (2000).

Soft Matter Keywords

Charged interfaces, Hydrodynamic coupling, Colloidal spheres, Modelling, Image forces, Colloidal Dispersion


Colloidal spheres are used as a simple model for studying the behavior of charged particles in a salt solution. It has been experimentally observed, contrary to intuition, that colloidal spheres with the same charge in a salt solution will attract each other, rather than repel. Many theories have been suggested for this observed behavior, however they have all involved including some sort of thermodynamic attraction. The authors provide a model for this effect near a single charged wall in terms of image forces, similar to the method of image charges in electrostatics.

Figure 1 - Two spheres forced away from a wall are drawn together by hydrodynamic coupling, because the flow due to one sphere’s image force pulls the other sphere towards it.


The model that the authors present is as follows. When the spheres are sufficiently close to the wall, they are electrostatically repelled from it. The net force on each sphere includes both their mutual electrostatic repulsion and their repulsion from the wall. How the spheres respond depends on their hydrodynamic mobility: when the spheres are close together (Fig. 2a), their mutual repulsion overwhelms any hydrodynamic coupling, and the spheres will separate as expected for like-charged bodies. However, when they are beyond some critical separation (Fig. 2b), the hydrodynamic coupling due to the wall force overcomes the electrostatic repulsion, so that the relative distance between the spheres decreases as they move away from the wall.

Figure 2 - (a) If the screening clouds of the two spheres overlap sufficiently, the mutual repulsion is stronger than the hydro- dynamic coupling. (b) When the spheres are farther apart, the hydrodynamic coupling dominates.


The behavior of charged particles in a salt solution is extremely important to the study of biological systems, and therefore soft matter. It is believed that the model of colloidal spheres can be extended to predict the behavior of DNA and proteins in a cell, which are similarly sized charged objects in a salt solution. The authors find that their model qualitatively agrees with experimental observations, however it should be noted that the theory only hold for situations where there is a force pushing the spheres off the wall. The theory does however provide an explanation for the observation that the attraction disappears when the salt concentration is increased.

--Cassidy 16:54, 16 September 2009 (UTC)